Here’s the long post. To HF, I’ll get to the above question, but I feel I need to cover the following topics in order to give the best answers to that question.. .. .After a fair amount of looking into this, it’s become clear to me that the physics community is in a state of serious confusion regarding “real” and “apparent” forces, with physicists and other scientists hotly debating the issues of what forces are “real” and what forces are “apparent”. I think the Coriolis “force” is a good example to illustrate this problem. This following example will also illustrate my personal frustration with the lose use of the word “apparent”, that some people are using as a label for some very real natural forces.. .. .Suppose you have a merry-go-round (turning counter-clockwise as seen from above) that has a putting cup for a golf ball right in the center of the turntable. Suppose there’s a chair on the outer edge of the turntable arranged facing inward, so that a guy sitting in the chair would look directly at the putting cup. Now suppose there’s a platform right next to the turntable, arranged with the edge of the platform level with and nearly touching the rotating turntable. Now imagine there’s a guy with a putter who strokes a golf ball into the cup in the center of the rotating turntable. Assume the turntable’s surface is quite low friction.. .. .To the guy with the putter, the golf ball appears to go straight into the cup. But to the guy sitting in the chair, the golf ball appears to be taking a left turning, inwardly directed spiral path into the cup. To him, the golf ball “appeared” to have been moved by a “force” that directed the ball to the left in a circular motion around the turntable. To this observer, the motion also appeared to have an inwardly directed component that eventually moved the golf ball, in its spiraling path, towards the cup.. .. .Both men observed the same event, but from very different “perspectives”. In my study it seems clear that these observational “perspectives” are referred to in the physics community as “reference frames”. More on this will follow later.. .. .The “apparent” motion that the man sitting in the chair observed is called the “Coriolis effect”. I found an interesting formula for the “Coriolis effect”, caused by the earth’s rotation on its axis, on an oceanographic and atmospheric website. It looks like this:. .. .C = fV. .. .Where “C” is the “Coriolis force”, V is the velocity, and “f” is the “Coriolis parameter”.. .. .The Coriolis parameter is defined as (I have to insert the words for the Greek symbols): f = 2(omega)sin(phi) where,. .. .(omega) is the angular velocity of the earth rotating on its axis (~ 7.3 x10(-5) rad/sec, and. .. .(phi) is the lattitude (either positive or negative, thus left or right visual effects for the 2 hemispheres).. .. .Notice that in the language of this website (and in the formula), the Coriolis “effect” is referred to as the Coriolis “force”. It is not a real force, but is in fact an observed effect on motion, since observers on earth are “observing” oceanic and atmospheric phenomena while sitting on a rotating earth. This is just like the guy sitting in the chair on the merry-go-round. The guys who do oceanic and atmospheric research have to take this “visual effect” (and motion effect) into account, thus the reason for the above formula’s existence. . .. .But I have problems with the language. First of all, it’s incorrect to call this observational effect a “force”, and since it’s not really a force (and we have to correct for this), we now have to call it an “apparent” force. “Apparent” is a word that can mean, “appearing as such but not necessarily so”. References to the Coriolis “force” are all over the Internet and I assume in textbooks also. This is a kind of “double corrective language” that in my opinion is a source of great confusion, which we will see later.. .. .REFERENCE FRAMES. .. .Now to reference frames. There are basically 3 type of reference frames, inertial, non-inertial, and free body. The following definition for an “inertial” reference frame from the Harcourt Dictionary of Science and Technology should help.. .. .inertial frame of reference Mechanics. a frame of reference that will allow Newton's laws to be valid in describing the motion of a system; the frame must either be at rest or be translating with a constant velocity. . .. .Note that an “inertial” reference frame requires a “perspective” where the observer is either at rest, or moving at a constant speed. In a nutshell, “non-inertial” reference frames involve acceleration of the observer. A “free body” diagram is a specifically confined “perspective” whereby all other objects are “removed” from the “environment” so that only the object or body under study is of “visible” interest to the observer.. .. .To illustrate all 3 types, I’ll use an elevator example. Suppose you have a 25-floor hotel with a very large atrium, and glass elevators (visible to an observer within the atrium) that can traverse all the floors. Suppose a 200lb. man (the rider) gets into an elevator and rides it up and down inside the atrium. Suppose another person (the observer) wants to measure some of the forces involved in this process. To a large extent, the force data “the observer” is trying to measure would determine which “reference frame” he chose to use. All 3 types of reference frames are available in this example, and they are as follows:. .. .The “inertial” reference frame – The observation point (“the observer’s” location for taking measurements) could be any location inside the atrium where the moving elevator could be observed, and “the observer” himself is not undergoing any “accelerated” motion. Another possible “inertial” reference frame would exist if “the observer” was riding in a glass elevator next to “the rider’s” elevator, AND “the observer’s” elevator was in constant motion WHILE he was taking measurements.. .. .In the first “inertial” reference frame (standing on the atrium floor), “the observer” can take direct measurements of acceleration and velocity of “the rider’s” elevator without any corrective factors, since neither he himself nor his coordinate system (for measuring), are in motion.. .. .In the second “inertial” reference frame (“the observer’s” elevator in constant motion), the only corrective factor that needs to be applied in order to derive accurate data about the motion of “the rider’s” elevator, is an adjustment for the constant velocity of “the observer’s” elevator. We assume our intrepid “observer” knows the math. . .. .The “non-inertial” reference frame – Suppose “the observer” (in an elevator) chose to measure “the rider’s” elevator WHILE his elevator was either being accelerated from a stop, or was being decelerated to a stop. As most of you know, the acceleration (or deceleration) of an elevator is non-linear, meaning the rate of acceleration changes before either rest or a constant speed is reached. Now the math is much more complicated, and our intrepid observer necessarily requires a COMPLETE understanding of the acceleration involved in HIS elevator, so he can apply the appropriate corrective factors to derive ACCURATE data about the “the rider’s” elevator. His math skills now must be very good indeed. So as a general rule, “non-inertial” reference frames are avoided wherever possible, but sometimes they cannot be.. .. .Some of you may have figured out by now that our man sitting in the chair on the 18th-hole merry-go-round, is observing from a reference frame that involved his constant (directional) acceleration. To him, the golf ball is moving in an inward left-hand spiral towards the cup, while the man with the putter is in an “inertial” reference frame and can observe the true forces involved without visual distortion. The man-in-the-chair’s reference frame is clearly “non-inertial”, and is often called a “rotating reference frame”. But what if the poor guy has only this particular vantage point available to him, and he still wanted to understand the exact forces involved in moving the golf ball from the edge of the merry-go-round to the cup in the center. What corrective factor could he apply to his “observed” data to derive the correct data?. .. .The answer would be a modified version (and formula) of the Coriolis “effect” that the atmospheric and oceanic observers have to use. Suppose the surface of the merry-go-round were laid out with radial lines (extending from the cup to the outer edge) and radius lines (equally spaced concentric circles extending out from the cup), which could provided the man-in-the-chair observer with a coordinate system to measure the motion of the gold ball. His coordinate system for measuring then, would be in accelerated motion just as he is, and would be part of the “non-inertial” reference frame. This of course is just like the circumstances the atmospheric and oceanic observers find themselves in, and their coordinate system that moves in “accelerated motion” with them, is the earth’s latitude and longitude system.. .. .The Coriolis “effect” works in “rotating reference frames” and is quite useful as a corrective factor here. If the man-in-the-chair observer applied this “effect” as a (should I dare say it) “apparent force” in a motion-force vector arithmetic formula, he could then derive the correct path and force applied to the golf ball. The man with the putter however, can derive this information much more directly, since his “inertial” reference frame contains no acceleration distortion. As I said, some “non-inertial” reference frames cannot be avoided. Except for the privileged few that travel in outer space, the A&O observers have no choice but to use the “Coriolis effect” (or corrective factor) when observing atmospheric or oceanic phenomena, since they cannot get off of the earth’s merry-go-round.. .. .The free body diagram – Suppose “the observer” in our hotel was only interested in measuring the forces being applied to “the rider’s” body while he was riding in the elevator. “The observer” could chose to isolate the man (in a “perspective” sense) from all of the other objects in his environment, and concentrate solely on what’s happening to “the rider’s” body, while forces from the elevator ride are being applied to it. In a free body diagram, all other objects are removed, and only the forces (represented by arrows, vectors, and values) are applied to the “body” under study. However to accurately understand a “free body’s” reaction to external forces being applied to it, those external forces MUST be accurately understood and quantified. As Nick said, this is how rotor blades (and other helicopter parts) are designed. This method is commonly used in FEA (Finite Element Analysis) of structural parts, where a part’s reactions to the various external forces (expected to be applied to it), are under computer study.. .. .THE CENTRIFUGAL FORCE. .. .There are all kinds of forces operating in the natural world. Among them are inertial forces, which constitute the resistance of all types of matter to acceleration (expressed in Newton’s first law of motion). Let’s look at a “free body” diagram familiar to all pilots, the airplane with the 4 basics forces of flight shown on it (gravity, lift, thrust, and drag). The drag force is an inertial force, as it consists of the collective resistance of all the air molecules near the plane, that must be moved out of the way as the planes passes through that local area. In order for an air molecule to be moved, it MUST be accelerated so its state of motion can be changed, and the resistance to this acceleration by the molecules is the force called “drag”. You’ll note that in most cases the “drag” force does not exist if the “thrust” force does not exist.. .. .But some in the scientific community are arguing that “inertial” forces are “apparent” and therefore non-Newtonian. Where on earth they are getting this I don’t know, but it’s clearly wrong. Do you guys remember that old desktop artifact from the 70s with the 5 shiny steel balls suspended on “V” shaped strings all lined up in a row? Remember that if you lift up a ball on one end and then drop it, the energy from that ball is transferred to the ball on the opposite end, and it flies up. It’s the “inertia” (or momentum) of the first ball that caused the opposite ball to move. Tell me this not a real force as work, and that’s its not demonstrating Newton’s laws of motion!. .. .Here’s a quote that Lu gave us from Robert McFarland of Sikorsky in the first post of this thread…. .. .“It took awhile, but the response from our Rotorhead Design group is as follows: . .. ."When you set up a free body diagram of a rotating mass such as a blade, one force is in the direction toward the center of rotation (centripetal force), the other force is in the direction away from the center of rotation (centrifugal force). They are the same force, centrifugal being the more common term." . .. .We hope that this is helpful. . .. .Regards,. .Robert McFarland. .WCS HelpDesk. .Sikorsky Aircraft Corporation. .. .Notice that just like in the “free body” diagram of the airplane, we have 2 opposing forces being applied to the rotor blade, one towards the hub, and the other towards the tip. We know that one is the centripetal force, and the other is the centrifugal force, and one does not normally exist without the other. Just like “drag” in the airplane diagram, centrifugal force is also an inertial force, but this time resisting “directional” acceleration instead of “linear” acceleration, but “resisting” all the same. Just as “thrust” (the acceleration force) is different from “drag” (the inertial “acceleration resisting” force), so the “centripetal” force (the acceleration force) is different from the “centrifugal” force (the inertial “acceleration resisting” force).. .. .One last example, then I’ll close this very long post. Suppose you have car with a passenger sitting in the back seat next to the right rear door. Suppose the window of that door is rolled all the way down, and he has an ice cream cone with a very large scoop of ice cream on top. Suppose also that the scoop is very loosely attached to the cone. Now suppose the car suddenly enters into a hard .5g left hand turn around a roundabout, and the ice cream scoop suddenly detaches itself from the cone and goes flying out of the window.. .. .To the man sitting in the back seat of the turning car, what path to the ground does the ice cream scoop seem to take from his perspective? Keep in mind that his frame of reference is “non-inertial” since the car is turning and he with it. He would see the scoop moving away from the car in an arc that travels towards the rear of the car, and down to the ground. But to a guy standing outside the car on a curb, the path of the scoop will appear to travel in a straight line away from the car and arcing towards the ground only (due to gravity). The only “apparent force” here is the one that seems to make the scoop arc towards the rear of the car. This particular arc is caused by the visual distortion of the car’s directional acceleration in the left-hand turn. . .. .The centrifugal force that caused the ice cream scoop to detach from the cone is real (an inertial force that caused the scoop to resist its acceleration around the roundabout). But the “apparent force” that seemed to cause the scoop to arc towards the rear of the car is not. A corrective factor could be applied to what the car passenger saw (and measured), then the true path of the scoop could be known to him.. .. .I hope this clears things up. If not, I tried my best.. .. .HF, I hope this discussion sheds some light on your question regarding steps 13 and 14 in your logic chain. This explanation would be the clearest answer that I think I could possibly give to that question.. .. .(edited for clarity). . . . <small>[ 18 March 2002, 06:30: Message edited by: Flight Safety ]</small>